Quadratic Common Lyapunov Fonction design for planar linear switched system stabilization

This paper gives a new approach about the stabilization of switched systems by Common Lyapunov Function (CLF), using mathematical tools from the plane geometry. In section II, a new necessary and sufficient condition about the stabilizability of switched systems is given. Then, the stability and geometric properties of a stabilizable planar linear switched system are presented. The section III is dedicated to the design of a Quadratic Common Lyapunov Function (QCLF) for planar linear switched systems, switching between two stable subsystems. This function can be seen as a control variable of the stabilized switched system.